aTV Flash (black) 2.2 is compatible with any ATV2 running 4.4 and later, so updating to 5.2 is not required. However, should you so desire, the best way to update can be found below.

Backup your settings through the Maintenance > Manage Backups menu.
Run the latest version of Seas0nPass to update the Apple TV to 5.2.
Download and install the new 2.2 version of aTV Flash (black).
Install any desired items through the Maintenance > Manage Extras menu.
Restore the previously saved settings through the Maintenance > Manage Backups menu.
That’s it!